Density functional theory

Density functional theory:

Solving large-scale quantum problems is very hard, but having a solution is very valuable since it can inform the better creation of materials and lead to revolutions in designs (for example, topological states of matter for quantum computing).

A theorem that was proven in 1964 shows that there is some hope of reducing the complexity in solving the quantum problems. Instead of using the wavefunction, the one-body density can be used instead. This essentially reduces the number of variables needed to describe a quantum problem while still describing the features of the ground state.

At present, the exact density functional must be approximated, but understanding better how the density functional must be used is vital to making better approximations. Our research is generally focused on finding the properties of the exact, universal functional instead of approximating it. However, we have invested time in demonstrating the ability for machine learning to learn the functional, including a proposal to do this on the quantum computer.


  • T.E. Baker and D. Poulin, "Density functionals and Kohn-Sham potentials with minimal wavefunction preparations on a quantum computer" Phys. Rev. Research 2, 043238 (2020) [online] [arxiv:2008.05592] [pdf] [bibtex]

  • J. Hollingsworth, L. Li (李力), T.E. Baker, and K. Burke, "Can exact conditions improve machine-learned density functionals?" J. Chem. Phys. 148, 241743 (2018) [online] [pdf] [bibtex]

  • Doctoral thesis, Methods of Calculation with the Exact Density Functional using the Renormalization Group (2017) [online] [pdf] [bibtex]

  • T.E. Baker, K. Burke, and S.R. White, "Accurate correlation energies in one-dimensional systems from small system-adapted basis functions" Phys. Rev. B 97, 085129 (2018) [online] [arxiv:1709.03460] [pdf] [bibtex]

  • A. Tkatchenko, M. Afzal, C, Anderson, T. Baker, R. Banisch, S. Chiama, C. Draxl, M. Haghighatlari, F. Heidar-Zadeh, M. Hirn, J. Hoja, O. Isayev, R. Kondor, L. Li, Y. Li, G. Martyna, M. Meila, K.S. Ruiz, M. Rupp, H. Sauceda, A. Shapeev, M. Stöhr, K.-R. Müller, S. Shankar, Recent Progress and Open Problems--Program on Machine Learning & Many-Particle Systems [online] [pdf] [bibtex]

  • C.J. García-Cervera and T.E. Baker, Mathematical Foundations of Quantum Mechanics (The IPAM Book of DFT) [pdf] [bibtex]

  • J.P. Perdew and T.E. Baker, Generalized Gradient Approximations (The IPAM Book of DFT) [pdf] [bibtex]

  • L. Li (李力), T.E. Baker, S.R. White, and K. Burke, "Pure density functional for strong correlations and the thermodynamic limit from machine learning" Phys. Rev. B 94, 245129 (2016) [online] [arxiv:1609.03705] [pdf] [bibtex]

  • T.E. Baker, E.M. Stoudenmire, L.O. Wagner, K. Burke, and S.R. White, "One dimensional mimicking of electronic structure: the case for exponentials" Phys. Rev. B 91, 235141 (2015) [online] [arxiv:1506.05620] [pdf] [bibtex]

  • L.O. Wagner, T.E. Baker, E.M. Stoudenmire, K. Burke, and S.R. White, "Kohn-Sham calculations with the exact functional" Phys. Rev. B 90, 045109 (2014) [Editor's choice] [online] [arxiv:1405.0864] [pdf] [bibtex]